Here is a simple method using which you can easily download music from YouTube :)
Do it at your own risk.
1. Go to Youtube - https://www.youtube.com
2. Search and copy the url of the song you want to download.
3. Go to http://www.youtube-mp3.org/
4. Enter the url in the box on the website.
5. Click on the 'convert video' button.
6. Then click on the 'download' button.
And the download should begin.
Step 2: Another Option/website
In some cases, the website mentioned above may not be able to convert the video to mp3 format and an error stating so may show up. In that case, you can use plenty of other websites with conversion capabilities.
1. A similar website is: http://www.clipconverter.cc/
2. Just like in the case of the website mentioned above, copy the video's url and paste it on the "video url to download box".
3. Select the conversion format to mp3 and then click on the "continue" button.
4. Then, click on the "start" button and your mp3 file should be ready to download!